Finally, we are able to state the R-linear convergence result under Assumption REF , which closely follows the line of the proof of [1]}. The key parts of the proof are the bounds on the gradient components from Lemma REF  and Lemma REF , the result on the \((\ell +1)\) st gradient component of Lemma REF . Our contribution is to adapt all these results that were already in [1]} but derived from [1]}. A slightly less general proof of R-linear convergence was previously presented in [4]}.
